Let f : C →Ĉ be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f (z) and proved, among others, that if f (z) has a Baker wandering domain U , then for all sufficiently large n, f n (U ) contains a round annulus whose module tends to infinity as n → ∞ and so for some 0 < d < 1,
M c (r, a, f ) d m c (r, a, f ), r ∈ G,where G is a set of positive numbers with infinite logarithmic measure. Therefore, we give out several criterion conditions for non-existence of the Baker wandering domains. 2005 Elsevier Inc. All rights reserved.